Mr Markle, 73, said he hoped the interview would ‘set the record straight’ after he was exposed colluding with a paparazzi photographer in the run-up to last month’s wedding to set up a series of faked photographs.

He then pulled out of giving his daughter away because of the negative publicity and a heart problem.

But the Sun on Sunday claimed his hopes that the interview would smooth things over seem to have been dashed because he has heard nothing from Kensington Palace since. He is also said to be upset that his daughter did not send him a card for Father’s Day, which is celebrated on the same day in both Britain and the US.

The newspaper quoted a source as saying: ‘There has been nothing from the palaces, which he is surprised about. He just hopes the interview hasn’t affected things. He wanted to discuss travelling to the UK, or the couple visiting him. He still hasn’t met Harry, and is desperate for it to happen.’

Kensington Palace declined to comment last night.

Mr Markle was paid £7,500 and flown to a luxury hotel in California from his home in Mexico to speak to the ITV breakfast show about his daughter and the wedding.

The interview came weeks after Meghan issued a public statement, describing the relationship between them as ‘deeply personal’. She and Harry also pleaded for ‘understanding and respect to be extended to Mr Markle in this difficult situation’.

In his interview he said Harry had told him he was ‘open’ to Brexit and that people needed to ‘give Trump a chance’. He also said he gave his permission for the couple to wed as long as the prince promised never to ‘raise his hand’ against his daughter.

Mr Markle admitted it had been a ‘mistake’ to accept money from the paparazzi to collude over pictures and that he had apologised to the couple, who forgave him.

He also said he thought the newlyweds want a baby ‘sooner rather than later’.

Although the palace declined to comment, it was clear that Harry and Meghan had been left disappointed and embarrassed by Mr Markle’s interview.